What are some real-world examples of compressible fluid mechanics in action?

AI Thread Summary
The discussion focuses on the compressible Euler Equations, highlighting their relevance in fluid mechanics. Participants seek real-world examples of these equations in action, particularly in non-1D scenarios. There is a specific interest in identifying pairs of functions that satisfy the equations while providing non-trivial solutions. The conversation emphasizes the need for practical applications of compressible fluid dynamics. Overall, the thread aims to deepen understanding of complex fluid behavior through concrete examples.
dcs23
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Hi Guys,

I know that the compressible Euler Equations are:

\partial_t (\rho \mathbf u) + (\mathbf u \cdot \nabla)(\rho \mathbf u) + \nabla p = 0

\partial_t \rho + \nabla \cdot (\rho \mathbf u) = 0

Subject to suitable initial conditions and solving for \mathbf u, \; \rho unknown.

Does anybody have an example of a pair of functions which satisfies these relations in a non-1D case?
 
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